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Proof step 90 from proof inv-format (previous step)

# buf = lptsize(# lpt, LEB_SIZE), # buf = lptlebs(# lpt, LEB_SIZE) * LEB_SIZE, avol = fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))], avol = avol, avol1 = avol, buf0 = buf, m2 = lptlebs(# lpt, LEB_SIZE), n0 = 5, ebm-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)), ebm-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), ebm-vol-inv(avol), is-encoded(lpt, buf), 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol ⊦ [persistence_io_write_lebs#(5, lptlebs(# lpt, LEB_SIZE), buf, LEB_SIZE; avol; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # avol = # avol1 ∧ ebm-vol-inv(avol) ∧ range=(avol, 0, avol1, 0, n0) ∧ range=(avol, n0 + m2, avol1, n0 + m2, # avol - n0 + m2) ∧ (err = ESUCCESS → lebs(avol, n0, m2) = buf0 ∧ mapped-full?(avol, n0, m2)) → ⟪m0 := EB_PAGE_SIZE; sb := ((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)); m := LEB_SIZE; if err = ESUCCESS then persistence_io_write_superblock#(sb, m0, m; avol; err); logoff := m⟫ ( ( err = ESUCCESS → (∃ lpt0, log, orphans. disk-layout(sb, # lpt0) ∧ sb.main + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb, avol[0].data) ∧ avol[sb.orph].mapped? ∧ is-encoded-pad(orphans, sb.orphsize, avol[sb.orph].data) ∧ avol[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb.log].data = logoff) ∧ is-encoded(log, avol[sb.log].data) ∧ mapped-full?(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)))) ∧ m0 = EB_PAGE_SIZE ∧ m = LEB_SIZE ∧ ebm-vol-inv(avol)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb.indexaddr = adr ∧ sb.maxino = m1 ∧ subarray(avol, sb.main, # avol - sb.main) = fill(mkavolume(# lpt), unmapped) ∧ is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE))) ∧ avol[sb.log].data = mkbuf(0) ∧ avol[sb.orph].data = mkbuf(0))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: rangeeq-concrete-unfold: m ≠ 0 ⊦ range=(avol, (* n), avol0, (* n), (* m)) ↔ avol[n] = avol0[n] ∧ range=(avol, n + 1, avol0, n + 1, m - 1);%nat-stuff2: ⊦ n = 5 + n1 → n ≠ 0;%nat-stuff3: ⊦ n = 5 + n1 → n ≠ 1;%rangeeq-write-right-concrete-below: n0 < n ⊦ range=(avol, (* n) + m, avol0[(* n0), aleb], (* n) + m, m1) ↔ range=(avol, n + m, avol0, n + m, m1);%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ m ≤ m + n; (s)% ⊦ m < n → avol[m, aleb][n] = avol[n]; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%m < # avol ⊦ avol[m, aleb][m] = aleb; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)%m ≠ n ⊦ avol[(* m), aleb][(* n)] = avol[n]; (s)% ⊦ range=(avol, n0, avol0, n1, 0) ↔ n0 ≤ # avol ∧ n1 ≤ # avol0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%m1 ≠ 0 ⊦ m ≤ (* m1) * m + n0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ # mkavolume(n) = n; (s)% ⊦ # fill(avol, aleb) = # avol; (s)% ⊦ # avol[n, aleb] = # avol; (s)